G is the group 243gp38
G has 3 minimal generators, rank 4 and exponent 9. The centre has rank 2.
The 13 maximal subgroups are: M27xC3 (3x), 81gp3 (9x), V81.
There is one conjugacy class of maximal elementary abelian subgroups. Each maximal elementary abelian has rank 4.
At present no information on the cohomology ring.